Abstract : Certain multi-level resource allocation problems can be modeled as concave-convex two-person zero-sum games which are additively separable except for the presence of coupling resource constraints. A decomposition principle is presented whereby solving such a problem is reduced to solving a dual problem followed by some modified subproblems, each of which has much lower dimensionality. Both the original and the dual problem are also related to an equivalent Lagrangian problem. These results are based on a recent extension of Fenchel's Duality Theorem to minimax problems. (Author)